Question

The average mark scored by 50 students in a class were calculated to be 38.later it found ,that marks of two students were wrongly copied as 34&23 instead of 43 and 32. Find correct average marks

Answer 1

Gien that, Average marks of 50 students = 38.

Now,

Mean = (Sum of all observations)/(Total number of observations)

Let us assume that the sum of all observations is M.

So,

⇒ 38 = M/50

⇒ M = 50(38)

⇒ M = 1900

Also, marks of two students were wrongly copied as 34 and 23 instead of 43 and 32.

Sum of all observations = 1900

Wrongly copied numbers = 34 and 23

Subtract the wrongly copied numbers from the sum of all observations.

⇒ 1900 - (34 + 23)

⇒ 1900 - 57 = 1843

New numbers = 43 and 32

Add the new numbers to the sum of all observations

⇒ 1843 + (43 + 32)

⇒ 1843 + 75 = 1918

From above calculations, we have new sum = 1918

Now,

New mean = (New sum)/(Total number of observations)

⇒ 1918/50 = 38.36

Answer 2

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$\green{\tt{\therefore{Correct\:average\:marks\:=\:38.36}}}$

$\pink{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

Given,

• Average of 50 students in a class = 38.
• Marks or two students were wrongly copied as 34 and 23 in place of 43 and 32 respectively.

Mean = $\frac{Sum\:of\:all\:observations}{Number\:of\: observation}$

Let the sum of all observations be x.

According to the question,

⇛38 = $\frac{x}{50}$

⇛ x = 38 × 50

⇛ x = 1900

Now, subtract the sum of wrongly copied number from the total sum(x).

⇛ 1900 - ( 34 + 23)

⇛ 1900 - 57

⇛ 1843

Now, add the sum of correct number to the total sum

⇛ 1843 + (43 + 32)

⇛ 1842 + 75

⇛ 1918

∴ New sum is = 1918

New mean = $\frac{1918}{50}$ = 38.36